Higgs branch

**superalgebra** and (synthetic ) **supergeometry**

For N=2 D=4 super Yang-Mills theory the moduli space of vacuum expectation values (VEVs) of the theory is locally a Cartesian product between the space of moduli of the vector multiplet (the gauge field sector) and those of the hypermultiplet (the matter field sector). The former is called the Coulomb branch, and the latter the *Higgs branch. These are dual to each other to it under a version of mirror symmetry .*

This is the topic of Seiberg-Witten theory.

Definitions of the Coulomb and Higgs branches have been extended to N=4 D=3 super Yang-Mills theory.

The terminology “Coulomb branch” and “Higgs branch” first appears in

- Nathan Seiberg, Edward Witten,
*Monopoles, Duality and Chiral Symmetry Breaking in $N=2$ Supersymmetric QCD*(arXiv:hep-th/9408099)

Quick exposition of the basic idea includes

- Cecilia Albertsson, around p. 31 of
*Superconformal D-branes and moduli spaces*(arXiv:hep-th/0305188)

On mirror symmetry between Higgs branches/Coulomb branches of D=3 N=4 super Yang-Mills theory (with emphasis of Hilbert schemes of points):

- Jan de Boer, Kentaro Hori, Hirosi Ooguri, Yaron Oz,
*Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes*, Nucl. Phys. B493:101-147, 1997 (arXiv:hep-th/9611063)

Last revised on December 29, 2019 at 18:26:25. See the history of this page for a list of all contributions to it.